Answer:
[tex]h(x)=2(x + 3)^{\frac{1}{2} }[/tex]
Step-by-step explanation:
Parent function of the square root function has been given as,
f(x) = [tex]x^{\frac{1}{2} }[/tex]
If the graph of the given function is stretched vertically by the scale factor = g(x) = [tex]k(x^\frac{1}{2})[/tex]
If the graph is shifted 3 units to the left,
h(x) = [tex]k(x + 3)^{\frac{1}{2} }[/tex]
Since, the graph of the function passes through a point (-2, 2),
[tex]2=k(-2 + 3)^\frac{1}{2}[/tex]
2 = k
Therefore, the function is [tex]h(x)=2(x + 3)^{\frac{1}{2} }[/tex].
